Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
22050.2-b3
22050.2-b
$8$
$12$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
22050.2
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)
\( 2^{8} \cdot 3^{12} \cdot 5^{12} \cdot 7^{4} \)
$3.07989$
$(a), (-a-1), (a-1), (5), (7)$
$1$
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2^{5} \cdot 3^{3} \)
$2.059609550$
$0.297372254$
5.196986521
\( \frac{21302308926361}{8930250000} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -578\) , \( 2756\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-578{x}+2756$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.